Hello @Yoonieman
WiFi client devices decide which access point to connect to and when to switch between them. Google/Nest WiFi (including Nest WiFi Pro) support some optional standards (802.11k and 802.11v) that provide WiFi client devices with extra information that can help them make better decisions about which access point to connect to and which to switch to when those devices have moved. However, many WiFi client devices do not support these standards, and they may end up getting "stuck" to an access point that is still working even when a better option is closer. I suspect that's what's happening here (though there is at least one other possibility). To verify, try opening the Google Home app, then tap on "Wifi", then open the devices list and find your phone in the list. Tap on it in that list and then switch to the "Info" tab. Under "Device Information", the name of the current "Point" that device is connected to should be a strong clue. If it's showing the name of a distant access point, then the device just isn't switching between access points, and you may have to briefly disable WiFi on that device to get it to switch. This is not a Google/Nest WiFi limitation, to be clear – it's an issue with the phone.
However, if it is showing as being connected to the nearby access point, but is still getting a poor signal (you can see that in the "Device information" section as well), then I would start to suspect a potential source of interference in the area. Soundbars with wireless subwoofers / surround speaker support are notorious for this in the 5GHz band.
I hope this information is helpful.
